We thank referee 1 for his review of our paper. We particularly appreciate the critical and detailed analysis he made and we think that taking these remarks into account will bring real added value to the paper. In particular, this will allow us to provide more illustrations of the modelling steps and better highlight the work we have done. In the following, we have taken up all the remarks, questions and suggestions made by referee 1 and numbered them from 1 to 10 for general comments. Sometimes comments have been subdivided into sub-sections in order to respond specifically to each suggestion. This is the case for general comments 7 and 9. Referee 1’s comment is given in bold and our response follows the comment in plain text

General comment 1 : The manuscript deals with the modelling of flood damage to agriculture, one of the (relatively) less investigated sector among the exposed assets. Although this makes the paper a potentially interesting contribution for NHESS, it actually suffers from several criticalities that, in my opinion, prevent its publication in its current version.

• We would like to thank referee 1 for his interest in the problematic of the article. We hope that the answers to the comments will improve the quality of the article so that it can be published.

General comment 2 : I would suggest the Authors to reconsider the way they presented their work, by better emphasizing the modelling aspects related to the proposed tool (floodam.agri), rather than presenting a ‘philosophical’ paper, with limited usefulness.

• We do not share referee 1’s assertion that this is a philosophical article. On the contrary, with this article we want to propose a reflection on the methodology of process-based model development which is based on strong field experience and is articulated with strong operational needs. It seems to us that referee 1 has not perceived the operational scope in our description of the methodological approach and its application. We will try to make this aspect more explicit, particularly in the description of the case study.

General Comment 3 : the actual structure of the manuscript makes it very confusing, with repetitions

• We agree with referee 1 and we will carefully consider this comment and ensure that redundancies are removed.

General Comment 4 : the article does not give the right emphasis on the model itself and on its innovation, which should be the main core of the paper. I would therefore re-arrange the structure of the manuscript by first presenting the model (with more details on it) and then explaining why it should be considered a “good” model and what are its current limitations.

• floodam.agri model is currently described in details in a French report (Agenais et al, 2013¹). For this reason, we do not wish to make the floodam.agri model the core of the article but rather an illustration of the fact that applying a rigorous methodology makes it possible to consider a reuse and/or an adaptation of the generic parts of the process-based model with a feeding of specific data (at different scales and on different contexts).

General comment 5 : On the contrary, the Authors just presented a description of the “archetype of a model” and then they try to explain (with limited success) why their proposed model should be considered as “the” model.

• Our ambition in the article was not to present floodam.agri as “the right model”. We will carefully review the article to avoid this being implied. We are well aware that very efficient models have been developed before, in particular the models developed by the FHRC and the AGDAM model developed by the USACE. We wanted to share our experience here because these process-based models are difficult to reuse because they are too context specific. We developed floodam.agri between 2010 and 2013 to be able to produce damage functions on a national scale because it was impossible for us to directly reuse existing process-based models in the French context. We really think that the modelling effort we have made could be reused and capitalised at the international level. But for this to happen, it seems to us that a rigorous methodological framework is needed.

General comment 6: In particular, the first part of the manuscript is very general, since the definition of the methodological framework for the development of a process-based flood damage model (Table 1) is not “new”, given that the listed questions are typically taken into account in the development phase of any process-based model.

• Based on our experience and the review of existing literature, we believe that this methodological contribution is necessary. From our point of view, although many initiatives to develop process-based models have been carried out, we are not aware of a methodology to capitalise on the development of process-based models. We will take this remark into account by insisting on this point in the literature review associated with the presentation of the framework. We will be very careful to include in the literature review any additional element concerning this point that referee 1 may communicate to us.

General comment 7 : More importantly, the way the Authors presented their model is also not very convincing. Indeed, unfortunately, when presenting floodam.agri, they failed in properly addressing some of the questions raised by themselves. I especially refer to the ones labelled as “Axis 1: explicit assumptions”, i.e. model and data transparency, which (I agree with them) should be regarded as one of the most important features of a model. I just mention hereafter some examples related to the lack of details on modelling assumptions within the model.

• We agree with referee 1 that the description of floodam.agri lacks in its current state a concrete example that would better highlight how assumptions are taken into account in a more pedagogical way. The main difficulty we have encountered is to account for the extent of all the phenomena dealt with in a systematic way over all the families of crops present in France. However, we agree that, as things stand, the explanation of the assumptions is not sufficiently illustrated in our article. In response to this remark, we propose to take the example of a rather complex crop, the apple in arboriculture, since several biophysical processes and behaviours are involved. This will allow us to illustrate the various points listed by referee 1 in the form of a box. For other crops, we propose to refer to the report Agenais et al (2013).
• GC 7.1: biophysical process taken into account to develop crop susceptibility functions: if you heavily claim for explicitness, the only Table 4 cannot be considered enough, but I would expect a thorough description on how the crop susceptibility functions were developed from a methodological point of view (e.g. by also considering a few crops as example and explaining how the different processes impact on the produced functions: i.e. how the plots reported in Figure 1 have been derived? (why I observe abrupt changes in damage at certain water depths and duration thresholds? Which are the driving mechanisms for these specific patterns?). I think this would be very interesting to know from a modeler’s perspective and this could be a real added value to the manuscript.
  • Using the example of apples in arboriculture, we will show how the data collected during the interviews and focus groups was implemented in terms of yield and quality variation. For example, we will show the graphs of yield variation for this crop (p227 to 228 of our report) and describe the biophysical processes mentioned by the experts (e.g. at the flowering stage, yield decreases are mainly due to root asphyxia…). We will also indicate the processes taken into account for the variation in quality by specifying the uncertainties expressed by the experts and the way we have dealt with them.
• GC 7.2: interviews with experts: no detailed information is provided within the manuscript on how the Authors actually took advantage of experts’ knowledge for developing floodam.agri. Again, I would suggest you to better describe the following aspects: how the questionnaires were structured (templates may also be included as supplementary material), how the collected data were analyzed and, in particular, whether you found uncertainty in the collected data and you handled this uncertainty in developing the model. Moreover, (if I understood correctly) the same experts were involved both in the development as well as in the “validation” (I would suggest not using this word) stage of the model: doesn’t this introduce a bias in the results of model “validation”?
  • We propose to put the interview grid developed for arboriculture and the materials discussed during the interviews (vegetative cycles) with the experts and translated into English in an appendix. We could also annex the presentation materials proposed to the experts during the arboriculture focus group.
  • Referee 1 is right to point out that there may have been divergent versions of the damage or variations in intermediate consumption collected in interviews with the experts. This is why we used the focus group method for the validation phase of our model. During the focus groups, the experts were able to discuss the assumptions and reach a consensus. Sometimes, processes had not been sufficiently explained in individual interviews. In this sense, we propose to give elements of the report of the focus group that was conducted on arboriculture. In particular, we will list, as an example, the elements that were modified following this focus group for the parameters of the model for apple crop.
  • Although referee 1 suggests not to use the word validation, we think it is important to keep this term as it seems to us an essential step which is missing most of the time in process-based modelling approaches due to lack of time or methodology. However, we found that when we reformulated and modelled the hypotheses formulated by the experts, modifications could be made. We propose to introduce the term partial validation to take into account referee 1’s remark.
• GC 7.3: farmers’ decisions: I would find interesting to know if you could report more (quantitative) details on the driving factors for farmers’ behaviors.
  • We will respond to this comment of referee 1 in conjunction with comment GC2.1 of referee 2. We propose to create a synthetic table that lists all the possible behaviours of farmers according to the crops considered. In addition, we propose to illustrate these behaviours with the case of apple crop.
• GC 7.4: the description of damage to soil should be better explained: it is not clear how tilling and cleaning are assessed, as I would expect these to be highly influenced (minimum) by the hazard parameters, soil and crop type. The modelling of damage to the equipment needs to be better clarified as well.
  • We propose to put in the biophysical processes section an illustrative table of how soil damage has been taken into account for arboriculture according to flooding parameters. Then in the decisions related to soil section we give the working times and values assigned for each level of damage (translation of table C.11 p238 of the Agenais 2013 report).
• GC 7.5: could you provide details on how the flood impact to the quality of the crops is modelled in floodam.agri?
  • The answer to the question concerning the quality of the crops will be dealt with under remark 6.1.

General comment 8 : The Authors may reply to my comments raised above that it would be impossible to provide full details of a (complex) model within a Journal paper, with limited available space. This is true, but, at the same time, you cannot claim a full lack of transparency (as you are experiencing also with your paper) of other models in the literature, by also mentioning this as the reason from writing the present article. So, the Authors’ comment on this point (P8-L186-189) appears to me a bit subjective (and not fair), given that the citated Agride-c is a well documented, explicit model, which seems to be originated by the same need for model transparency claimed by the Authors.

• We agree with referee 1 that it is impossible to give all the modelling assumptions for all the crops treated. We believe that the proposal to treat the apple crop in an exemplary way and to refer to the Agenais report (2013) and to the online damage functions² for the other crops makes it possible to answer this remark.
• Concerning Agride-c and its presentation in Molinari et al. (2019) and Scorzini et al. (2020), we did not write that there was a full lack of transparency in presenting this model, this assertion seems to us excessive. It turns out that this model can be seen as a transfer from floodam.agri to the Italian context as it is largely based on the work presented in Agenais et al (2013). Indeed, the crop damage coefficients that largely determine the damage are directly adapted from Agenais et al, 2013. Similarly, the crop pursuit strategies and soil damage are very similar to what was proposed in Agenais et al, 2013. We have expressed the idea, without elaborating on it, that this transfer was not carried out in a way that allows for capitalisation. For example, the “validation” part by the local experts consulted is not documented in a sufficient way to understand what are the limits of the assumptions retained in floodam.agri for the Italian context. One possibility is that the description of floodam.agri was not explicit enough to discuss these assumptions, which is one of the reasons for writing our article. We propose to make this point more explicit.

General comment 9 : Another aspect that would deserve more attention is the actual applicability of the model. The Authors mentioned that floodam.agri has been already applied in France in several projects. It would be then very valuable if you could give more details on these experiences, e.g. which were the main difficulties for application, necessary adaptations and/or assumptions in the input data (for both hydraulic and vulnerability / exposure data). Indeed, floodam.agri, as any micro-scale process-based model, requires very detailed input data, with some of them usually not know/difficult to know or with high local variability, then necessarily requesting some kind of averaging or simplification process in order to make the model actually applicable at the river basin/ reach scale.

• Referee 1’s remark GC9 suggests that it is not completely clear that floodam.agri is a model for producing damage functions at different scales. In the paper, we show how we used floodam.agri to produce national damage functions in France. These damage functions were parameterised for use in cost-benefit analyses of flood management projects in France. We used national databases to estimate yields, prices, intermediate consumptions… (Table 9 and 10). The important steps for the production of ready-to-use FDFs were steps 3 and 4 in Figure 4 as they were necessary to make the FDFs compatible with the database for spatial location of crops (RPG). We propose to explicitly answer questions GC9.1 and GC 9.2 as follows.
• GC 9.1: how the problem of crop rotations was handled for identifying crop type in each plot?
• For the national application, we proposed to create a mixed function to manage rotations if necessary on the application territory. If the 3-year rotation is wheat, wheat, rape, the weight assigned to the wheat function is 2/3 and the weight assigned to rape 1/3. This explanation will be added in the section case study/ready to use flood damage functions.
• GC 9.2: In which month of the year the flood was supposed to occur in the damage calculations (did they consider the month with the highest probability of flood occurrence / or did they calculate a weighted average damage, with the weights represented by the probabilities of flood occurrence in each specific month ?)
• For the national application, it was proposed to simplify the season parameter and we defined 4 seasons whose periods are specified in table 12. The consultancy firms that carry out cost-benefit analyses have the possibility, if their hydrological model allows them, to produce the agricultural damages for these 4 seasons within the framework of the CBA. However, in the model, the time step is the week, which leaves the possibility of adjusting to the local context. This explanation will be added in the section case study/ready to use flood damage functions.

General comment 10: I finally do not agree with the statement at P27.L615-616 (as well as the one in the abstract, P1.L5-8), or I may did not interpret well the Authors’ point, which I then ask to be better clarified. According to me, the model framework must be certainly general, but, especially when modelling damage to agriculture, it is strictly necessary to be context- specific, in order to capture the typical features of the region where the model is applied, otherwise we are oversimplifying reality, which can be an acceptable solution (a “full adaptation” may be a huge effort, since while some components can be easily adapted (e.g. yields and price values), there are others that highly change from a context to another (e.g. the cultivation practices and operations)), but that we must be aware of it

• Referee 1’s comment GC 10 suggests that it is not yet clear enough in the article at this stage which parts are generic and which are inputs, intermediate inputs and outputs. We propose to address this by improving Figure 4 and 5 by merging them and making the above explicit. In particular, our major contribution is to model damage processes and behaviours that are thought to be generic because they are based on the vegetative cycle of the crops that can be calibrated for each study case on the weeks of the year. We will explain this point around figure 4. Concerning the adaptation to another context, we propose to add a reflection on the perspectives in terms of applicability on a micro scale and the reflections that arise in terms of variability of behaviours (adaptation to floods, variability of technical itineraries).

Minor comment: although the sense is always clear and English usage is almost correct, the paper needs to be proofread as there many typos (e.g. “litterature”, “diven”, “developped”, just to cite some) and few weird sentences (e.g. P2.L24, P2.L41).

• We are aware that English still needs to be improved. We have tried to make our words as clear as possible in this non-native language. We thank referee 1 for pointing out the typos, which will be corrected. Knowing the publication process of NHESS, we have full confidence that the final review process of English, in which we will be fully involved, will achieve the necessary language standards.

We would like to thank referee 2 for the analytical work that was done on our paper. We thank him for his encouragement to publish this work and for all the suggestions and questions that were formulated and that will allow us to improve this paper.

In the following, we have numbered the general comments from 1 to 5. Sometimes comments have been subdivided into sub-sections in order to respond specifically to each suggestion. This is the case for the general comment 3. Then specific comments (SC) are numbered from 1 to 6. One technical comment seemed to us to require a more detailed response and we have added it to the specific comments. This is the SC 6. Referee 2’s comment is given in bold and our response follows the comment in plain text. All technical comments will be taken into account without the need for a specific response

General comment 1 : The authors propose a methodological framework to understand under which conditions expert knowledge used to fed process-based models of flood damage assessment are valid. Their framework is based on 4 axes: explication of assumptions, validation, updatability and transferability. an application is proposed in France for the agricultural sector. The focus given to the agricultural sector is well justified by the fact that agricultural lands are often flooded to reduce urban flood risk. Assessing flood damage is thus key to evaluate the efficiency of this measure and the compensation given to farmers. This article is very valuable contribution because it proposes a framework for flood damage assessment which is generalizable and it claims to make explicit the assumptions used in such models. Furthermore, it proposes an open source model for flood damage assessment in agriculture in the form of a R package, to be available soon.

• We thank referee 2 who encourages us to publish this work which seems to us important to go towards a mutualisation and a capitalisation of the modelling effort to better evaluate the impacts of floods.

General comment 2: The model is applied to the agricultural sector. It is restricted to the plant farming. What about livestock? Is this also applicable to this sector of agriculture? It could be discussed

• At present, floodam.agri has not been used to produce damage functions for the livestock sector. However, floodam.agri can be used to produce damage functions for grasslands. Regarding the impacts on livestock, interviews were conducted with experts. However, these inputs have not yet been modelled. We propose to take this into account at two levels. Firstly, in section 4.1, we propose to add the cattle component to the farm entity and to make it clear that, as things stand, the damage functions produced do not estimate the impacts on animals. Secondly, we propose to add in section 5 (Discussions), a remark on the potential for improvement and future developments envisaged around floodam.agri (integration of herds, coupling with floodam.building for the consideration of buildings).

General Comment 3: on taking into account the farmer’s decisions in the model

• GC 3.1: When I look at your system of decision I cannot see a symmetry between the crop and plant material systems. You include the possibility to change the crop type in equation 8 but not for plant materials. One should also have the case of a farmer who decides to plant another type of trees, similarly to equation 8 for crops.
  • Concerning adaptation decisions, this is a very pertinent remark which invites us to better explain in the article the consideration of farmers’ behaviour in the face of floods. In the current damage functions produced with the floodam.agri model, adaptations such as crop changes are not taken into account. The underlying assumption is that of a continuity of the current type of production. There is no change of crops (annual or perennial) in the strategic sense. Behavioural adaptations are at the level of the rotation, the technical itinerary or replanting decisions. Crop changes as described in equation (8) only concern field crops that are usually grown by farmers in rotation. If a flood occurs in winter and destroys the autumn planted crop, the field crop farmer still has the opportunity to plant a spring crop. It is not a question of switching to market gardening or viticulture, for example. All these hypotheses on the usual adaptation strategies during the production cycle were constructed and validated with the experts. A change in production type, even for annual crops (e.g. field crops to market gardening), implies a broader strategic change at the farm level (equipment, inputs, inclusion in a production chain, training), the determinants of which are still poorly understood. However, we are well aware, and we were able to meet with farmers during our field interviews, that these adaptation strategies can be implemented, especially when farmers are subjected to recurrent events on sensitive crops such as arboriculture. We propose to take this observation into account at several levels.
  • First, in section 4.1, we will clearly explain the assumption of continuation of the current activity and reconstruction used for all components to produce the current damage functions with floodam.agri.
  • Secondly, in the paragraph dedicated to the description of the decisions related to crops, we will make more explicit the behaviors that we have retained on the basis of our interviews with the experts. We propose to make a table summarising the decision rules according to the types of crops. In addition, we will give examples with the apple crop chosen as an example in response to referee 1’s comments.
  • Thirdly, based on the example of field crops, we propose to detail more explicitly the strategies for continuing the itinerary, reseeding, sowing a spring crop, abandonment, which were defined on the basis of discussions with the experts.
  • Fourthly, we propose, as in the response to comment 1, to describe the prospects for improvement around floodam.agri and in particular a discussion around the question of adaptation to the meaning of flood risk by changing the crop on a plot (conversion from vineyard or cereals to grassland) and the implication in terms of economic evaluation.
• GC 3.2: It seems to me that not all the post flood decisions made by farmers should be taken into account in the model otherwise you overestimate the damage. This is particularly the case when farmers decide to do something different from what they were doing before the flood (like in equations 8 and 12, sowing another crop or not replanting). In this case, the variation of revenues is not a damage because the reference has changed. The pre and post yields are not comparable, Y_new is different than Y_u because it is another crop, not because the biophysical conditions have changed in the farm because of the flood. If a farmer decides not to replant trees or crop, for example because he/she stops the activity or because she/he wants to invest in another farming activity or other species for example, then the damage function (eq 8, eq 12) is rather an opportunity cost or possibly a benefit rather than a damage. Counting equation 8 and 12 as a damage creates opportunities for farmers to operate a change in their agroecosystem and ask for money to the damage compensation organism for that change because they have been flooded. But the reason is not the flood, the reason can be economic or another reason. This will also have the perverse effect of making farmers prefer to wait to be flooded to change their agroecosystem to receive more money (in the case where they are compensated based on your damage functions.) This does not mean that the famer cannot anymore change the crop system after a flood, but it means that the compensation based on the damage function should not pay for the change but pay for what has been lost. To pay for the change brings your model to the context of adaption to climate change, not a context of compensation for flood damage. One could imagine a farmer willing change species in order to use species more resilient for floods because floods become more frequent or more devastating. This is possible but this is not what your paper is proposing. Your paper is about compensation, not adaptation. This should be discussed or corrected.
  • The answer to the previous question seems to us to partly answer the questions formulated concerning annual crops.
  • For perennial crops, I should clarify that in the non-replanting strategy, there is no option not to replant the plot at all. It is a matter of not replanting the missing trees. Beyond a certain number of missing trees, the decision rule is to uproot and replant the whole plot. This will be mentioned more explicitly in the article and as suggested by referee 1 will be illustrated with the case of apple crop in arboriculture.
  • For field crops, where there is the option of planting a new crop with a Y_new, in no case can the product be higher than a conventional campaign since the sowing and some costs will already have been incurred. The behaviour summary table should make this more explicit.
  • The application of floodam.agri proposed in this article does not aim to propose a method of compensating farmers. The application of floodam.agri presented in the article is an application that aims to develop large-scale damage functions for damage assessment (project CBA). For an application aiming at compensations in the case of overexposure protocols for example, local data should be specified. Furthermore, in this case, it could be considered locally to define crops less sensitive to flooding and to set up compensations to farmers, but this is not the purpose of our article.

General comment 4: Section 4.2 validation: V2 on comparability with other models (uk , Italy, etc). Maybe you can compare the conceptual approaches between UK, Italy and France. This can help you to also highlight the contributions of your model to the literature. By literature I do not mean the case study based literature (filling the gap of having a model for the French agriculture) but the literature on the structure of flood damage assessment models (ie your figure 8). For example, is it usual to integrate decision rules in the calculation of damage or the biophysical processes? This kind of comparison will improve your contributions (in addition to the contribution of making explicit the assumptions) and the value of the paper for an international readership.

• We thank referee 2 for this suggestion, which we believe to be very relevant. This table could be a summary of how the axes of the conceptual framework are treated in the following models : FHRC model, AGDAM developped by USACE, Agride-C model and in floodam.agri.

General comment 5: I recommend to have the paper revised by a native English speaker: grammar, use of the article “the” (the figure x , the table x versus Table x, Figure x), etc.

• We are aware that English still needs to be improved. We have tried to make our words as clear as possible in this non-native language. Knowing the publication process of NHESS, we have full confidence that the final review process of English, in which we will be fully involved, will achieve the necessary language standards.

Specific comments

• SC1: Tables are at the end of the paper (except Table 1) and figures in the main text. Are the tables part of an appendix or to be included in main text? If they have to be part of an appendix, please check the guidelines for authors.
• The latex format proposed for the submission of the preprint has automatically placed some of the figures and tables at the end of the document. This should not be the case for a final version. We will check this with NHESS technical support.
• SC2: Plant material or perennial crops? You have related plant material to perennial crops line 318 but you have an equation for perennial crops in the section related to crops and then several equations in a section on plant material. This is confusing.
• Plant material is attached to perennial crops (e.g. apple trees for apple crop) but crop losses depend on farmers’ decisions to replant plant material. Yield loss on plots depends on the proportion of damaged trees and decisions to replant or not. We propose to make this more explicit by adding a diagram and making the summary table of behaviours and associated equations as proposed earlier.
• SC3: Equation 8: What happens if Y_new > Y_u? It is no more a damage but a benefit. Does this mean that the farmer will revert money to the compensation fund because she/he earns money after the flood? This should be discussed or a constraint should appear in the system of equations
• As explained earlier, the possibility of sowing a new crop only arises for cereals when the flooding occurs too late for the previous crop to be resown and early enough for a spring crop to be sown. This is not optimal, but it does compensate for some of the costs incurred. We propose to explain this point in the article.
• SC4: Section Decision related to soil. It seems to me that you should also discuss the case of a variation in soil quality because of the flood (example of chemical pollution, or loss oforganic matter of the first layer of the soil). This affects yield also. Does this correspond to equation 6? Or would this be a case of double counting if you add an equation for that?
• Soil damage such as pollution, salinisation and loss of organic matter have not been included in floodam.agri for the time being. The main reason for this is that there is no physical model to establish a correlation between flooding and pollution or loss of organic matter. Furthermore, the experts consulted indicated that they were unable to establish correlations between the hazard parameters and these biophysical processes. We thank referee 2 for this remark which will allow us to support the soil part in the physical processes section (EA2).
• SC5: Figure 8. Following my concern about accounting for decision rules and actions in the modelling of the damage functions. My concern is now visual: depending on the decision/action, the farmers has the possibility to increase the damage if he/she chooses the appropriate action. To maximise the damage and so the future compensation can become a strategy for the farmers in this model. This is a perverse strategy in my sense but your model allows it if I understand it well. The damage should be based on past losses not on future losses in case of changing practices. I am Ok with accounting for future losses in case of deterioration of soil quality, or in case of sowing the same crop again
• We hope to have answered this question in the previous answers. The confusion is related to this option of changing crops which is only valid for field crops in rotation.
• SC6 : Farm building. Is the cadastre a possible source for the data on agricultural buildings? What are the limitations to not use it if it exists?
• The land register allows to locate buildings but not to know their use (housing, shed, silo…). The BD TOPO could be an improvement. However, it seems to us that it would be important to be able to link the types of crops to farm buildings. Indeed, from our modelling experience (floodam.building and FDF to companies) for economic activities, damage to buildings is largely linked to the equipment and stocks present and therefore to the nature of the activity. We propose to address this comment in the perspectives of improvement of floodam.agri.

Technical corrections

We thank referee 2 for his technical corrections that we will all take into account.